The past few days have seen anti-government protesters on the streets of Egypt, Jordan and Yemen – inspired in each case by the uprising that toppled President Zine el Abidine Ben Ali in Tunisia. In Algiers, riot police also suppressed a planned march calling for the president's resignation which had been organised by the Rally for Culture and Democracy, a secular party with strong Berber connections.

There have been disturbances, too, in Lebanon but they are a continuation of old sectarian/political rivalries rather than anything strikingly new. The emerging popular struggles to oust entrenched autocrats are the ones to be watched most closely.

Egypt: the big one

The huge demonstrations in Egypt yesterday didn't come entirely out of the blue. Strikes and street protests have long been a feature of Egyptian life and the political debate there is far more open than it was in Tunisia. The shock yesterday was in the scale of the protests – far beyond what the authorities and even the organisers expected, and all that without much support from the traditional opposition parties (including the Muslim Brotherhood which had declined to give its formal backing).

As in Tunisia, the protests were largely secular and instigated by the Facebook generation – the 6 April Youth Movement and Kifaya ("Enough") – along with trade unionists.

There were many allusions to Tunisia in yesterday's protests. Add to that the economic situation in Egypt, the blatantly rigged (and widely mocked) parliamentary election last month, an 82-year-old president who has spent 30 years in power and seems intent on handing over to his son, years of repression by the regime, frustrated youth and a general sense this can't go on much longer – and you have all the ingredients for rebellion.

Where does it go from here? Unless President Hosni Mubarak dies of fright or agrees to step down in the meantime, the struggle that began so spectacularly yesterday is likely to continue until the presidential election in October (or, depending on the outcome, possibly beyond it).

The Mubarak regime appears more solidly based than Ben Ali's in Tunisia and its security apparatus has plenty of experience in controlling discontent. Nevertheless, they seem to have been outmanoeuvred in places yesterday and there were some reported instances of demonstrators fraternising with the police.

For the moment, the opposition parties seem content to let Mubarak serve out his term so long as he doesn't stand again or install his son, Gamal. The Wafd – Egypt's most-established legal party – last night called for a national unity government and fresh parliamentary elections under proportional representation.

No doubt the struggle will have its ups and downs, but I do sense that the question now is when change will come to Egypt, not if it will happen. I wouldn't place any bets on Mubarak senior staying in power beyond October and the prospects for Mubarak junior are surely receding by the day. As in Tunisia, though, dismantling Mubarak's political machine, along with his web of patronage and corruption, will be a tougher nut to crack.

Jordan: bread and freedom

For the second Friday in succession there were protests in Jordan, though on a fairly small scale. "Bread and freedom" was one of the slogans, along with calls for the government to resign. Economic grievances were the spur, and the Islamic Action Front (the local arm of the Muslim Brotherhood) seems to have played a prominent role.

Complaining about the king is still taboo in Jordan, so the protests focused on his ministers, even though it is the king who actually pulls the strings. Jordan still has a long way to go before there can be anything that might be considered as regime change and the difficulties of achieving it are compounded by the population split between Palestinian elements and the tribal Bedouin elements.

Yemen: a question of succession

Turmoil and armed rebellions are so much a part of everyday life in Yemen that a few thousand students and opposition activists demonstrating at Sana'a University might not seem especially significant. But they were calling, very directly, for President Ali Abdullah Salih to go – and alluding, once again, to events in Tunisia.

The presidential issue in Yemen is the same as in Egypt, though slightly less immediate. Salih has been in power in Sana'a for 32 years and the constitution says he must leave office in 2013. Salih shows no intention of stepping down (he's trying to change the constitution so that he can stay) and, like Mubarak, appears to be grooming his son, Ahmed, to succeed him.

Yemenis have a strong republican tradition (having thrown out their king in the 1960s with Egyptian help) and they don't like the idea of a hereditary presidency at all. The country remains hopelessly divided by politics and tribalism but this is one issue around which people may possibly, over the next couple of years, be able to unite.